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The question asks if lines \( L_1 \) and \( L_2 \) in the graph are parallel, based on their slopes.

### Explanation:

To determine if two lines are parallel, we need to compare their slopes. Two lines are parallel if and only if they have the same slope.

#### Finding the slope of \( L_1 \):
From the graph, the points on \( L_1 \) are \( (0, -5) \) and \( (8, -2) \). The slope of a line can be found using the formula:

\[
\text{slope of } L_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-5)}{8 - 0} = \frac{-2 + 5}{8} = \frac{3}{8}
\]

#### Finding the slope of \( L_2 \):
The points on \( L_2 \) are \( (0, 1) \) and \( (-6, 2) \). Applying the slope formula again:

\[
\text{slope of } L_2 = \frac{2 - 1}{-6 - 0} = \frac{1}{-6} = -\frac{1}{6}
\]

#### Conclusion:
The slopes of \( L_1 \) and \( L_2 \) are \( \frac{3}{8} \) and \( -\frac{1}{6} \), respectively. Since these slopes are not equal, the lines are **not parallel**.

Thus, the correct answer is **A**: No, lines \( L_1 \) and \( L_2 \) are not parallel because they have different slopes.

Would you like more details or further explanations?

### Related Questions:
1. What happens if two lines have the same slope but different y-intercepts?
2. How can you determine if two lines are perpendicular based on their slopes?
3. What is the significance of the negative sign in a slope?
4. How can you find the slope of a line from an equation rather than points?
5. How can parallel lines be useful in geometric proofs?

### Tip:
Always check for sign errors when calculating slopes, especially when subtracting negative numbers!

In the graph to the right, are lines L1 and L2 parallel? Explain.

Analyze whether lines L1 and L2 are parallel by calculating their slopes. This problem uses the slope formula and the parallel lines theorem to determine that the lines are not parallel because their slopes differ. Suitable for students in Grades 8-10.

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